Scilab Function
Last update : 12/1/2004

freq - frequency response

### Calling Sequence

  `[x]=freq(A,B,C [,D],f)`
  `[x]=freq(NUM,DEN,f)`

### Parameters

- `A, B, C, D`: real matrices of respective dimensions `nxn, nxp, mxn, mxp`.
- `NUM,DEN`: polynomial matrices of dimension `mxp`
- `x`: real or complex matrix

### Description

`x=freq(A,B,C [,D],f)` returns a real or complex `mxp*t` matrix such that:

`x(:,k*p:(k+1)*p)= C*inv(f(k)*eye()-A)*B + D`.

Thus, for `f` taking values along the imaginary axis or on the unit circle `x` is the continuous or discrete time frequency response of `(A,B,C,D)`.

`x=freq(NUM,DEN,f)` returns a real or complex matrix `x` such that columns `k*(p-1)+1` to `k*p` of `x` contain the matrix `NUM(f(k))./DEN(f(k))`

### Examples

    s=poly(0,'s');
    sys=(s+1)/(s^3-5*s+4)
    rep=freq(sys("num"),sys("den"),[0,0.9,1.1,2,3,10,20])
    [horner(sys,0),horner(sys,20)]
    //
    Sys=tf2ss(sys);
    [A,B,C,D]=abcd(Sys);
    freq(A,B,C,[0,0.9,1.1,2,3,10,20])

### See Also

`repfreq`, `horner`,